264 TKANSACTIONS OF THE SOCIETY OF 



M. Galopin has given us a metliod of determining the maxima and 

 the minima of a function. It consists in reducing to the derivative of 

 the function, and then arranging the roots in the order of their powers. 

 In tliis order they correspond alternately to a maximum and a mini- 

 mum, so that it is only necessary to determine the derivative of one of 

 them. 



M. de la Harpe has exhibited a property of numbers by which it results 

 that the cube of one number is always equal to the difference of the 

 squares of two other numbers. 



We commence the enumeration of the works of the society in physical 

 science proper, with meteorology. 



M. Plantamour has given a summary of the udometric observations 

 for the meteorological year 1872. From the commencement of our 

 regular observations, that is to say, from the year 1826, there has never 

 been as much rain in one year as in that of 1872. The aun ual mean at 

 Geneva is 824'^™. In 1872 there fell 1,080™™ ; that is to say, over a third 

 more than the mean. 



M. Plantamour has kept the society informed in regard to the geodetic 

 operations carried on in Switzerland. The purpose of the geodetic cam- 

 paign of 1872 has been to determine the co-ordinates of the Gebris, 

 in the canton of Appenzell, the Gebris being one of the points of the 

 new international triangulatiou, intended to connect this mountain with 

 the Austrian triangulatiou. An error in the closing of a large polygon 

 l^assing through the Simi)lon and the Gothard necessitated a new set of 

 operations, for there was an error in taking the level of about 1™, which 

 was inadmissible. The cause of this error has not yet been discovered. 

 The errors which are found out by the closing of a polygon have also 

 been the subject of a communication from General Dufour, who has 

 mentioned the deviation of the plumb-line, on account of the neigh- 

 borhood of the mountains, as a possible cause of the want of accord- 

 ance between the two levelings. 



Our society, in concert with the Vaudois Society of Natural Sciences, 

 has decided, as you know, to undertake an examination of the bottom 

 of the lake. In view of this work, MM. A. Favre and 11. Hentsch have 

 made some preparatory soundings, which have been the subject of a 

 communication to the society. The process of determining a profile by 

 soundings, which consists in causing an experienced rower to give the 

 same number of strokes of the oar between two consecutive soundings, 

 is not sufficiently precise ; at least it did not prove to be so under the 

 conditions in which the observations were made. Under other circum- 

 stances it might be useful. If, on the contrary, the profile is obtained by 

 means of a rope supported by corks, results may be corrected by a 

 second operation. The depth of the little lake is in some parts much 

 greater than is indicated in the map of the canton. 



I am constrained to mention in this connection the communication by 

 M. Chaix of a hydrographic map, published by the federal bureau, to 



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